That is right. Downy Woodpeckers do not sing like most birds. They communicate by “pecking” or drumming on wood or even metal. Surprisingly these woodpeckers make very little or no sound when going after their insect prey. They are capable of feeding on insects that larger woodpeckers cannot catch, like fly larvae in weed stems.
We see both male and female Downy Woodpeckers quite often in our backyard. They like the suet feeders, and we have spotted a male on our hummingbird feeder. Like the White-breasted Nuthatch, Downy Woodpeckers like to flit from branch to branch, lighting on the suet feeder, grabbing a bite or two and then off they go.